Halimar Depths, chance of revealing n land, using my deck as an average layout.(*)
0: 20.8%
1: 44.2%
2: 29.0%
3: 5.9%
So, in the 0 case, we hold our Treasure Hunt, or time it to draw the good card at a irrelevant time.
In the 1 case, we get a draw two for sure, and can set it up to draw the land + non-revealing card this turn, next turn, or go for the ancestral recall two turns from now.
In the 2 case, I typically put the non-land on top, then cast TH the next turn for draw 3+.
In the 3 case, either you draw 4+ that turn, or you draw 3+ the next turn.
TH is exceptional in the 35% case where you draw 3 or more. (or 4 or more, depending).
The 1 land case takes up a huge chunk of the probability matrix, and gives you the most flexibility in your options. If you need the land and can draw now, you can do that, or you can set up the draw-2 (reveal less dangerous) next turn, or you can go for the gusto.
The 0 land hand (21%) is the one where TH is the "worst", but your current situation is probably the best. (Drawing 3 spells)
Now, lets look at some basic See Beyond(SB) math.
Number of lands in the top two cards:
0: 35.5%
1: 48.8%
2: 15.6%
Treasure Hunt is exceptional in the 0 case, which is a similar 35% that you'd see for TH above.
TH is "comparable" in worth to the 1 land on top case, in that you have to wait longer for SB to give you the 2 cards, in roughly the same percentage of the time.
What is our scenario in the bad case for See Beyond though. If SB is bad, we draw two land, shuffle the land we had in hand into the deck, and still have two land left over. This puts us in topdeck mode.
In the "bad" case for TH, we're drawing three useful spells without even casting anything, so we just don't cast our TH for a while, and get more use out of it later.
So, TH seems clearly superior in every case where we have a Halimar Depths anywhere in our future. (Thank you Deprive)
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What about if we don't have a Halimar Depths? What is our expected return off a blind TH?
Well, Treasure Hunt draws us one action card always, but the trick is how many land do we get.
This comes down to the chance that the top card is a land. This is about 40% with unknown card distribution.
But we also have the chance that if the top card is a land, that the next card is also a land (roughly 40% * 40%), or another 15.6%. Then we have the chance that the next card is also a land (another 6%), and the next card is also a land (2%), and so on.
This adds up to a little over 1.6 cards expected per Treasure Hunt.
Or, one "action" card, and .6 lands.
How does this compare to a "blind" See Beyond?
From the above chart:
Number of lands in the top two cards:
0: 35.5%
1: 48.8%
2: 15.6%
Presuming we shuffle the land back in, and don't have another land to shuffle in, this gets us an average of:
15.6%: 1 land
48.8%: 1 card
35.5%: 2 cards - our worst card at the time. (worth half a card lets say)
This puts our average draw at .16 lands + 1.02 cards This seems inferior to the blind TH, with the only advantage being 2% more cards, and hiding what cards you drew.
If we presume that we do have a 0-worth land to throw away, then we get:
15.6%: 1 land
48.8%: 1 card
35.5%: 2 cards
This puts our overall result at 1.55 cards + .16 lands -.355 land
This translates to a conversion of ~.5 of a land, into .55 of a card. Which is pretty good. Depending on the game state, we may take that trade. Early game, probably not, late game, probably.
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Secondary effects of both spells:
Treasure Hunt reveals your draws.
This is awkward in a deck with counterspells, but not fatal. It is worst when you draw a counterspell and it is your only card (~11% of the cards in the deck are counterspells), and have either no mana to play that card, or it is the only card in your hand, and you can't recover from the board position with a counterspell.
As a mitigating factor, See Beyond also can't recover by drawing a counterspell in the second situation, they can just hide that they drew it.
Very high level players can probably get some good usage out of this information, but the average player typically doesn't foresee what is going to happen with that card (bouncing own PA in response to removal for example), or it doesn't matter, because so many of the cards in the deck do the same thing. (CTM especially!)
If I reveal a Mana Leak (which is no longer in the deck), that is easily played around. If I reveal a Deprive, they may presume I also have Mana Leak (which any sane player would be playing now?), which means I get some good value despite what is normally the worst-case scenario for Treasure Hunt.
See Beyond shuffles your deck.
Normally, you'll have ~1 bad card scried to the bottom, and the one bad card in your hand you are shuffling back in, but you can still draw these cards. You have a continual ~4% chance each turn to draw those cards that you'd "dealt with" each turn.
Not ginormous, because you are eventually going to have to shuffle your deck anyway, with Scalding Tarn, just to get land out to play spells, but it is there.
The more Foresees you cast, the more Preordains, etc, the more important this factor gets. (When playing Foresee, I have scried ~8-10 cards to the bottom without clearly winning. It sure sucks to shuffle those back in.
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Overall Conclusions:
So, the Blind TH, vs the no-land SB seems to be a win for TH.
The Blind TH, vs the one-land SB leans slightly towards the SB (but with slightly reduced card quality going forward)
The HD + TH scenario clearly beats the SB scenario. early, late, and mid, because you end up with more cards in hand (that you can't waste draws on later), and your mana development isn't hindered.
If you think about it, the worst TH is not much worse than the average SB scenario. 66% of the time, you'll do no better than drawing one action card with SB, and some of the remainder, you will just be upgrading one card to another. Treasure Hunt always nets you even in cards, and guarantees a minimum of one good card, which See Beyond can't promise.
See Beyond and TH are not too far apart, there are some big overlaps where they do the same thing, and where one just has a slight edge over the other. I would just say that SB has more variance, which is probably not that useful. So, I'm sticking with my 4x TH + 4x HD, and trying out 4x Deprive to compliment them.
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(*)Average layout...
We presume that the deck starts at a ratio similar to 24 land, 60 total cards when we start looking at cards off the top of our deck. In reality, this will never be the ratio, but we have to start somewhere, and we can't draw general conclusions about how many land or non-land we'll have seen. This is a known problem in this type of analysis, and it probably can't be helped.
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